Preservice teachers' understandings of division and ratios in forming proportional relationships

This study aimed at investigating how preservice teachers' understandings of division and reasoning about ratios support and constrain their formation of proportional relationships in terms of quantities. Six preservice teachers from a middle-grade preparation program in the USA were selected purposefully based on their mathematics performance in a previous course. An explanatory case study with multiple cases was used to make comparisons within and across cases. Two semi-structured interviews were conducted with each pair. The results revealed that preservice teachers who did not explicitly identify different meanings for division struggled to differentiate between the two perspectives on ratios. The results also showed that those teachers had difficulty forming proportional relationships while solving the proportion tasks. These results suggest that explicit identification of the meanings for both types of division is critical to keeping the two perspectives on ratios separate, which is a key aspect for a robust understanding of proportional relationships.WOS:000771562400002Scopus - Affiliation ID: 60105072Emerging Sources Citation IndexArticle; Early AccessUluslararası işbirliği ile yapılmayan - HAYIRMarch2022YÖK - 2021-22Mar

Two Distinct Perspectives on Ratios: Additive and Multiplicative Relationships between Quantities

The purpose of this study is to investigate how pre-service teachers’ formation of additive and multiplicative relationships support and constrain their understandings of ratios and proportional relationships in terms of quantities. Six pre-service teachers were selected purposefully based on their performances in a previous course. An explanatory case study with multiple cases was used to make comparisons within and across cases. A semi-structured interview was conducted with pairs of pre-service teachers. The results revealed that pre-service teachers’ heavy reliance on additive or multiplicative relationships critically shaped their reasoning about ratios from the two perspectives. Pre-service teachers who only attended to multiplicative relationships were found to have a robust understanding of proportional relationships. Pre-service teachers, who did attend to additive relationships, even if they used multiplicative relationships, struggled to form appropriate proportional relationships from the two perspectives. 

Preservice teachers' math teaching anxiety in an online laboratory school

The purpose of this study was to examine preservice teachers’ math teaching anxiety, to explore the relationships between math teaching anxiety and several variables, and to understand how preservice teachers’ math teaching anxiety changed during eight-weeks of the Online Laboratory School (OLS) within a university. We administered the Math Teaching Anxiety scale with 14 items to 43 preservice teachers by adapting Hadley and Dorward’s (2011) scale. The results revealed that on average, preservice teachers had math teaching anxiety from “a little” to “a moderate amount” degree before the OLS and their math teaching anxiety did not significantly change during the OLS. Moreover, math teaching anxiety was only significantly correlated with the number of methods courses completed so far.Nisa

Enhancing prospective mathematics teachers’ noticing skills through online laboratory school activities

This study investigated how prospective mathematics teachers’ (PMT) noticing skills, (i.e., attending, interpretation, and decision-making) were influenced through online laboratory school (OLS) activities. OLS provided PMTs opportunities for online fieldwork and work with students. The activities included lesson planning with peers under the supervision of academicians and experienced teachers, teaching, reflection and getting feedback. PMTs’ reflections on a video-taped lesson served as the pre-post assessment of the intervention. Quantitative analyses of data indicated PMTs showed statistically significant improvement in both interpretation and decision-making. Attending, on the other hand, was improved but not in a statistically significant way.Temmu

Enhancing prospective mathematics teachers’ noticing skills through online laboratory school activities

This study investigated how prospective mathematics teachers’ (PMT) noticing skills, (i.e., attending, interpretation, and decision-making) were influenced through online laboratory school (OLS) activities. OLS provided PMTs opportunities for online fieldwork and work with students. The activities included lesson planning with peers under the supervision of academicians and experienced teachers, teaching, reflection and getting feedback. PMTs’ reflections on a video-taped lesson served as the pre-post assessment of the intervention. Quantitative analyses of data indicated PMTs showed statistically significant improvement in both interpretation and decision-making. Attending, on the other hand, was improved but not in a statistically significant way

Validation of the Math Anxiety Scale with the Rasch Measurement Model

WOS: 000465161900005The purpose of this study was to investigate the psychometric characteristics of the Math Anxiety Scale (MANX; Erol 1989, Unpublished master thesis, Bogazici University) with data collected from 952 middle school students in Turkey. The Rasch Rating Scale model was used to examine the MANX at the item level. The results revealed that although the MANX was sensitive to detect students with moderate levels of math anxiety and it was not targeted to identify those with very high and low math anxiety levels, it had high reliability and validity. Moreover, the majority of the MANX items were of good quality. The results of this study provide strong evidence for the validation of the MANX despite the need for deletion of eight misfit items and three items with the same item difficulties. Future research should consider possible revision or development of new items to capture gradations of challenges at the very high and low ends of the continuum

Validating psychometric classification of teachers' fraction arithmetic reasoning

National Science Foundation [DRL-0903411]The development of the Diagnosing Teacher's Multiplicative Reasoning (DTMR) Fractions survey was supported by the National Science Foundation under Grant No. DRL-0903411. The opinions expressed are those of the authors and do not necessarily reflect the views of NSFIn prior work, we fit the mixture Rasch model to item responses from a fractions survey administered to a nationwide sample of middle grades mathematics teachers in the United States. The mixture Rasch model located teachers on a continuous, unidimensional scale and fit best with 3 latent classes. We used item response data to generate initial interpretations of the reasoning characteristic of each latent class. Our results suggested increasing facility reasoning about fraction arithmetic from one class to the next. The present study contributes two further arguments for the validity of our initial interpretations. First, we administered the same survey to a new sample of future middle grades mathematics teachers before and after 20 weeks of instruction on multiplication, division, and fractions, and we found that from pretest to posttest future teachers transitioned from one latent class to another in ways consistent with increased proficiency in fraction arithmetic. Second, we interviewed 8 of the future teachers before and after the instruction and found that future teachers' reasoning during interviews was largely consistent with our original interpretation of the 3 latent classes. These results provide further support for our original interpretation of the mixture Rasch analysis, demonstrate the utility of our approach for capturing growth and change in future teachers' reasoning during teacher education coursework, and contribute innovative applications of psychometric models for surveying teachers' reasoning at scale.WOS:0009133913000012-s2.0-85146190901Social Sciences Citation IndexarticleUluslararası işbirliği ile yapılan - EVETŞubat2023YÖK - 2022-2

Teachers' Attention to and Flexibility with Referent Units

Attending to the whole unit that a number refers to in a mathematical problem situation and showing flexibility in coordinating different units are foundational for mathematical understanding. In this study, we explored teachers’ attention to and flexibility with referent units in situations involving fractions and fraction multiplication. Using data collected across the USA from 246 mathematics teachers in Grades 3–7 where fractions are taught, we found that teachers’ attention to and flexibility with referent units were related to each other as well as to teachers’ overall knowledge of fractions.WOS:000669290900001Scopus - Affiliation ID: 60105072Social Sciences Citation IndexQ3Article; Early AccessUluslararası işbirliği ile yapılan - EVETJuly2021YÖK - 2020-2

An Online Laboratory School research on pre-service mathematics teachers’ experiences and mathematics teaching anxiety

During the COVID-19 pandemic, we founded an Online Laboratory School (OLS) under the roof of a university in Turkey to support students from public schools that were not technologically prepared for an online education and to provide an opportunity for our pre-service teachers (PSTs) to continue their internship by teaching online. The purpose of this research, consisting of two studies, was to examine experiences of 43 PSTs (first-, third- and fourth-years) during the OLS period of 8 weeks and how the OLS affected their mathematics teaching anxiety during Fall 2020. In the first study, we administered a survey to inquire into PSTs’ views on their experiences at the OLS, and in the second study we examined their mathematics teaching anxiety before and after the OLS experience using another survey. One main result was that the OLS experience served as an effective introduction to the profession for first-year PSTs and fourth- and third-year PSTs reported learning in-depth about online teaching in terms of the planning, teaching, and reflecting cycle. Another main result was that PSTs had mathematics teaching anxiety from “a little” to “a moderate amount” before the OLS and their teaching anxiety did not significantly change during the OLS period of 8 weeks. PSTs experienced highest mathematics teaching anxiety when they were observed and evaluated by supervisors during their teaching. The implications of these findings are discussed for teacher education programs.Kası